1. Field of the invention
The present invention is related to volume rendering, which plays a very important role in the visualization of scalar data (volume data) defined over a three-dimensional (3-D) region.
2. Description of the Related Art
In volume rendering, a density cloud is displayed from volume data, and the appearance of the cloud can be easily modified by specifying a transfer function for mapping scalar data to opacity. With this technique, scientists and engineers have come to understand the overall distribution of volume data from various kinds of numerical simulation results and measurements.
Among volume rendering techniques presented so far there are the ray tracing method, the slice-by-slice method, and the tetrahedral projection method.
In the ray tracing method, a ray that passes each pixel is generated from a viewing point and the volume data is integrated along a viewing ray. Actually, values at several sampling points along the ray are approximated by numerical integration instead of by performing integration. There are two sampling methods. One is to sample data in equal intervals along the ray and the other is to evaluate points of intersection of ray and cell. The data to be handled is an orthogonal regular grid in the former sampling method, and the volume data to be defined on an irregular grid in the latter. The details are described in the following references. Reference (A) is related to the former sampling method and reference (B) is related to the latter.
(A) Levoy, M., "Display of Surfaces from Volume Data," IEEE Computer Graphics & Applications, Vol. 8, No. 3, pp. 29-37 (May 1988). PA1 (B) Garrity, M. P., "Raytracing Irregular Volume Data," Computer Graphics, Vol. 24, No. 5, pp. 35-40 (Nov. 1990). PA1 (C) Drebin, R. A., Carpenter, L., and Hanrahan, P., "Volume Rendering," Computer Graphics, Vol. 22, No. 4, pp. 65-74 (Aug. 1988). PA1 (D) Shirley, P. and Tuchman, A., "A Polygonal Approximation to Direct Scalar Volume Rendering," Computer Graphics, Vol. 24, No. 5, pp. 63-70 (Nov. 1990).
In the slice-by-slice method, color value and opacity volume are created from the volume data defined on the superlattice, and converted into a volume facing the viewing direction by the 3-D affine method, and then images are generated by composing surfaces (slices) from front to back or from back to front in order along a viewing ray using the two-dimensional (2-D) image composition method. This is the volume data defined on the superlattice. The details are disclosed in the following reference (C).
The tetrahedral projection method is a method aiming at effective use of a 3-D graphics processor that handles existing triangulated primitives for the purpose of increasing the processing speed. First, the original data is divided into tetrahedral cells. Here, using the silhouette of a tetrahedral cell projected on the screen, the original tetrahedral cell is further divided into smaller tetrahedral cells so that the projected image becomes a triangle. Then, colors and opacities are evaluated at the vertices of the triangles that are the projected images of the tetrahedral cell and the results are made into images as a set of triangles having color values and opacities at the three vertices using a graphics processor. This method is described in the following reference (D).
However, if an attempt is made to materialize an advanced display function using the conventional volume rendering techniques mentioned above, compared to the conventional surface rendering technique, it will take enormous amount of computation time with any of these techniques under the present conditions, because of the following two reasons. The first reason is that, in volume rendering, data sampling must be carried out over a 3-D region, unlike with surface rendering. The second reason is that, in surface rendering, dedicated processors for the purpose of increasing the processing speed have been developed and many of them have been put on the market as important component elements of engineering workstations, but with volume rendering, no such processors have yet been put on the market.
Also, in conventional volume rendering, there is a restriction in that the volume data to be handled is limited to either a regular grid or an irregular grid.
An object of the present invention is to provide a method that can materialize rendering processing from volume data at high speed using a surface rendering processor.
An0ther object of the present invention is to provide a rendering method having no restrictions on the structure of volume data to be processed.